Reduced costs obtained from the optimal simplex tableau are not necess
arily correct under degeneracy in network flow problems with side cons
traints. In one application, simplex reduced costs were shown not to b
e good when applied to actual operations, while reoptimization to find
all true reduced costs was too time-consuming. An efficient algorithm
to obtain approximate reduced costs was developed in the research to
offset these disadvantages. The algorithm combines the uses of Lagrang
ian relaxation, a minimum-cost network flow algorithm, and a shortest
path algorithm. In theory, the approximate reduced costs prove to be a
better lower bound than are simplex reduced costs. Numerical experime
nts have been performed to show its potential usefulness in practice.
(C) 1996 John Wiley & Sons, Inc.